Summary
We present a simple model based on microscopic automata to describe the clonal expansion process. The model is based on a repertoire of antigens and T lymphocytes interacting via antigen-presenting cells which present the antigens peptides. Each cell is represented by an automaton moving randomly on a two-dimensional lattice.We use this simplified model in order to introduce local and spatial considerations in the mathematical models of clonal expansion based on differential equations, and at the same time to attempt an analytical interpretation of the results of computer simulations. For this reason we also derive a mean field theory, whose results are in good agreement with the solutions of the microscopic model, at least for situations that are not too far from equilibrium. This model may be used as the basis of a more realistic one that could follow the clonal expansion process on a simplified version of the lymphatic network.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
De Boer, R., Perelson, A.S.: T cells repertoires and competitive exclusion. J. Theor. Biol., 169, 375–390 (1994).
Hofbauer, J., Sigmund, K.: Evolutionary Games and Population Dynamics. Cambridge University Press, London (1998).
Novak, M., May, R., Sigmund, K.: Immune responses against multiple epitopes. J. Theor. Biol., 175, 325–350 (1994).
Antia, R., Ganusov, V., Ahmed, R.: The role of models in understanding CD8+ T-cell memory. Nature Reviews Immunology (published online 20 January 2005).
De Boer, R., Perelson, A.S.: Competitive control of the self renewing T cell repertoire. International Immunology, Vol. 9, No. 5, p. 779, Oxford University Press, London (1997).
Lanzavecchia, A., Sallustio, F.: Lead and follow: the dance of the dentritic cell and T cell. Nature Immunology, 5, 1201–1202 (2004).
Hugues, S., Fetler, L., Bonifaz, L., Helft, J., Amblard, F., Amigorena, S.: Distinct T cell dynamics in lymph nodes during the induction of tolerance and immunity. Nature Immunology, 5, 1235–1242 (2004).
Lindquist, R., Shakhar, G., Dudziak, D., Wardemann, H., Eisenreich, T., Dustin, M., Nussenzweig, M.: Visualizing dendritic cell networks in vivo. Nature Immunology, 5, 1243–1247 (2004).
Germain, R., Jenkins, M.: In vivo antigen presentation. Current Opinion in Immunology, 16, 120–125.
Callard, R., Stark, J., Yates, A.: Fratricide: a mechanism for T memory-cell homeostasis. Trends in Immunology, 24, 370–375 (2003).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Birkhäuser Boston
About this chapter
Cite this chapter
Zanlungo, F., Rambaldi, S., Turchetti, G. (2008). An Automata-Based Microscopic Model Inspired by Clonal Expansion. In: Deutsch, A., et al. Mathematical Modeling of Biological Systems, Volume II. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4556-4_12
Download citation
DOI: https://doi.org/10.1007/978-0-8176-4556-4_12
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-4555-7
Online ISBN: 978-0-8176-4556-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)